PTCB Math Problems – Latest 2025/2026 Exam
Prep & Practice Questions
Assuming that the medication comes in 10ml vials, the days' supply for a prescription
that is written as Humalog U-100 Inject 10 U SQ QID would be
Hint: Cross multiply ( Humalog U-100 is a 10ml bottle that has 100U/ml) - correct
answer25 days
1st step (Units/ mL)
100U/1mL = U/10ml
100 x 10 = 1,000
1xU=U
X = 1,000U
2nd step (Injecting 10 units 4 times daily. multiply both)
40/1 day = 1,000U/x day
40 X x day= 40x
1 X 1,000 = 1,000
1,000/ 40x = 25
Ozempic 2mg/ 1 pen prescribed
"Inject 0.25 mg sc once weekly".
Solve day supply of insulin.
Hint: divide mg being injected by mg of drug then multiply by 7 ( because there's 7 days
in a week) - correct answer56 days
0.25mg/2mg = 8
8 x 7= 56 days
Ozempic 2mg/ 1 pen
"Inject 0.25mg sc once weekly for 4 weeks then inject 0.5 mg for 2 weeks "
Solve day supply of insulin
Hint: (Attempt to translate from pharmacist that just showed the work.) parentheses are
my comments. - correct answer42 days
1ST DOSE: 0.25mg sc once weekly for 4 weeks
Day supply: "28 days" (because 1st dose is for 4 weeks, 7 days in a week, and 7x4= 28)
,~ Ozempic 2mg / 1 pen.
0.25mg x 4 (weeks) = 1 mg (being used?)
2 (med) mg - 1mg (used) = 1 mg remaining
2ND DOSE: 0.5mg for 2 weeks.
~ Extra: "0.5mg x 2 weeks = 1 mg" ( qty needed to complete dose?)
Important:
2 (med) mg / 1 mg (remaining) = 2 mg
2 mg x 7 days = 14 days
3rd step
28 days + 14 days = 42 days
What will the flow rate be for an order written to administer 2 liters of an IV fluid over 18
hours?
A.) 56 mL/hr
B.) 83 mL/hr
C.) 111 mL/hr
D.) 101 ml/hr
Hint: Divide the volume by the time to get the flow rate (2 liters equals 2,000 mL) -
correct answerC.) 111mL/hr
What will the infusion rate be if a 500 mI IV bag is infused over 3.5 hours?
Hint: Divide given ml by hours then divide solution by 60 (60 minutes in an hour) to
convert answer to minute since answer choices are in minutes. - correct
answer2.38ml/min
500ml /3.5 hour = 142. 86
142. minutes= 2.38
An order is written for 500 mL of NS to infuse at 40 gtt/min. If the set delivers 10 gtt/mL,
how long would it take to infuse the NS?
A.) 100 minutes
B.) 40 minutes
C.) 50 minutes
D.) 125 minutes
Hint: multiply drops in set with mL prescribed then divide sum by flow rate - correct
answerD.) 125 minutes
10 gtt/mL means 10 drops per mL. So for
500 mL you will get:
10 × 500 = 5,000 drops
, The flow rate is 40 gtt/min, which means 40 drops per minute, so divide total drops by
40 to get the number of minutes:
5,000/40 = 125 minutes
Determine the flow rate to run 1 liter of D5W containing 10,000 units of heparin through
a set delivering 60 gtts/ml. (Heparin should be delivered at a rate of 25 units/min) -
correct answer150 gtts/min
How many pounds is equal to 5.5 kg?
A.) 1.21 16
B.) 0.55 lb
C.) 55 Ib
D.) 12.1 lb
Hint: Multiply (A kilogram is equal to 2.2 pounds) - correct answer2.2 x 5.5= 12.1lb
How much of each solution will be needed when you are planning to prepare 600 ml of
20% dextrose solution, by mixing your 5% and 50% dextrose solution?
A.) 300 mL of the 50% and 100 mL of the 5%
B.) 300 mL of the 50% and 300 mL of the 5%
C.) 350 mL of the 50% and 250 mL of the 5%
D.) 200 mL of the 50% and 400 mL of the 5%
Hint: Alligation problem so use "tic tac toe". Divide parts by total parts and then multiply
sum by amount of mL preparing - correct answerD.) 200 mL of the 50% and 400 mL of
the 5%
Put 50 in the upper left of your tic-tac-toe table, 5 in the lower left, and 20 in the middle.
Subtracting across the middle you will put 15 in the upper right (20-5=15) and 30 in the
lower right (50-20=30). So you need 15 parts of the 50% and 30 parts of the 5%, for a
total of 45 parts (30+15= 45).
50 | = | 15
__ | 20 | __
5 | = | 30 (@self you tried to do TicTacToe on phone)
Amount of 50% needed will be:
(15/45) × 600 = 200
Amount of 5% needed will be:
(30/45) × 600 = 400
How much dextrose is in a 900mL
solution of D5W?
A.) 180 g
B.) 90 g
C.) 45 g
D.) 500 g
Prep & Practice Questions
Assuming that the medication comes in 10ml vials, the days' supply for a prescription
that is written as Humalog U-100 Inject 10 U SQ QID would be
Hint: Cross multiply ( Humalog U-100 is a 10ml bottle that has 100U/ml) - correct
answer25 days
1st step (Units/ mL)
100U/1mL = U/10ml
100 x 10 = 1,000
1xU=U
X = 1,000U
2nd step (Injecting 10 units 4 times daily. multiply both)
40/1 day = 1,000U/x day
40 X x day= 40x
1 X 1,000 = 1,000
1,000/ 40x = 25
Ozempic 2mg/ 1 pen prescribed
"Inject 0.25 mg sc once weekly".
Solve day supply of insulin.
Hint: divide mg being injected by mg of drug then multiply by 7 ( because there's 7 days
in a week) - correct answer56 days
0.25mg/2mg = 8
8 x 7= 56 days
Ozempic 2mg/ 1 pen
"Inject 0.25mg sc once weekly for 4 weeks then inject 0.5 mg for 2 weeks "
Solve day supply of insulin
Hint: (Attempt to translate from pharmacist that just showed the work.) parentheses are
my comments. - correct answer42 days
1ST DOSE: 0.25mg sc once weekly for 4 weeks
Day supply: "28 days" (because 1st dose is for 4 weeks, 7 days in a week, and 7x4= 28)
,~ Ozempic 2mg / 1 pen.
0.25mg x 4 (weeks) = 1 mg (being used?)
2 (med) mg - 1mg (used) = 1 mg remaining
2ND DOSE: 0.5mg for 2 weeks.
~ Extra: "0.5mg x 2 weeks = 1 mg" ( qty needed to complete dose?)
Important:
2 (med) mg / 1 mg (remaining) = 2 mg
2 mg x 7 days = 14 days
3rd step
28 days + 14 days = 42 days
What will the flow rate be for an order written to administer 2 liters of an IV fluid over 18
hours?
A.) 56 mL/hr
B.) 83 mL/hr
C.) 111 mL/hr
D.) 101 ml/hr
Hint: Divide the volume by the time to get the flow rate (2 liters equals 2,000 mL) -
correct answerC.) 111mL/hr
What will the infusion rate be if a 500 mI IV bag is infused over 3.5 hours?
Hint: Divide given ml by hours then divide solution by 60 (60 minutes in an hour) to
convert answer to minute since answer choices are in minutes. - correct
answer2.38ml/min
500ml /3.5 hour = 142. 86
142. minutes= 2.38
An order is written for 500 mL of NS to infuse at 40 gtt/min. If the set delivers 10 gtt/mL,
how long would it take to infuse the NS?
A.) 100 minutes
B.) 40 minutes
C.) 50 minutes
D.) 125 minutes
Hint: multiply drops in set with mL prescribed then divide sum by flow rate - correct
answerD.) 125 minutes
10 gtt/mL means 10 drops per mL. So for
500 mL you will get:
10 × 500 = 5,000 drops
, The flow rate is 40 gtt/min, which means 40 drops per minute, so divide total drops by
40 to get the number of minutes:
5,000/40 = 125 minutes
Determine the flow rate to run 1 liter of D5W containing 10,000 units of heparin through
a set delivering 60 gtts/ml. (Heparin should be delivered at a rate of 25 units/min) -
correct answer150 gtts/min
How many pounds is equal to 5.5 kg?
A.) 1.21 16
B.) 0.55 lb
C.) 55 Ib
D.) 12.1 lb
Hint: Multiply (A kilogram is equal to 2.2 pounds) - correct answer2.2 x 5.5= 12.1lb
How much of each solution will be needed when you are planning to prepare 600 ml of
20% dextrose solution, by mixing your 5% and 50% dextrose solution?
A.) 300 mL of the 50% and 100 mL of the 5%
B.) 300 mL of the 50% and 300 mL of the 5%
C.) 350 mL of the 50% and 250 mL of the 5%
D.) 200 mL of the 50% and 400 mL of the 5%
Hint: Alligation problem so use "tic tac toe". Divide parts by total parts and then multiply
sum by amount of mL preparing - correct answerD.) 200 mL of the 50% and 400 mL of
the 5%
Put 50 in the upper left of your tic-tac-toe table, 5 in the lower left, and 20 in the middle.
Subtracting across the middle you will put 15 in the upper right (20-5=15) and 30 in the
lower right (50-20=30). So you need 15 parts of the 50% and 30 parts of the 5%, for a
total of 45 parts (30+15= 45).
50 | = | 15
__ | 20 | __
5 | = | 30 (@self you tried to do TicTacToe on phone)
Amount of 50% needed will be:
(15/45) × 600 = 200
Amount of 5% needed will be:
(30/45) × 600 = 400
How much dextrose is in a 900mL
solution of D5W?
A.) 180 g
B.) 90 g
C.) 45 g
D.) 500 g
